Solving Systems Word Problems with Matrices

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns, used to represent a system of equations.

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CCSS.HSA.REI.C.8

Front

How can matrices be used to solve systems of equations?

Back

Matrices can be used to represent systems of equations in a compact form, allowing for the application of matrix operations to find solutions.

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CCSS.HSA.REI.C.9

Front

What is the purpose of the augmented matrix?

Back

An augmented matrix combines the coefficients and constants of a system of equations into a single matrix, facilitating the use of row operations to solve the system.

Tags

CCSS.HSA.REI.C.8

Front

What is row reduction?

Back

Row reduction is a method used to simplify a matrix to its row echelon form or reduced row echelon form, making it easier to solve the system of equations.

Front

What is the difference between consistent and inconsistent systems?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

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CCSS.8.EE.C.8B

Front

What is a dependent system?

Back

A dependent system has infinitely many solutions, where the equations represent the same line or plane.

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CCSS.8.EE.C.8B

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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CCSS.HSA.CED.A.3

Front

What is the substitution method?

Back

The substitution method involves solving one equation for a variable and substituting that expression into another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6